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带双势的非线性Klein-Gordon方程驻波的不稳定性 被引量：1

Instability of Standing Wave for Nonlinear Klein-GordonEquations with Double Potentials
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摘要 研究了一类带双势的非线性Klein Gordon方程的柯西问题.首先利用变分法得出了具基态的驻波的存在性,然后根据这个结果证明了该驻波的不稳定性. Studied the Cauchy problem of a class of nonlinear Klein-Gordon equations with double potentials. The existence of standing wave with the ground state is obtained by variational calculus. Then the instability of the standing wave is proved.
作者 陈渝芝
机构地区 重庆工学院数理学院
出处 《四川大学学报（自然科学版）》 CAS CSCD 北大核心 2005年第2期253-258,共6页 Journal of Sichuan University(Natural Science Edition)
关键词 非线性Klein—Gordon方程 双势 驻波 不稳定性 nonlinear Klein-Gordon equations double potentials standing wave instability
分类号 O175.26 [理学—基础数学]
  • 相关文献

参考文献8

  • 1Zhang J. On the standing wave in coupled nonlinear Klein-Gordon equations[J]. Math. Meth. Appl. Sci, 2003, 26:11-25.
  • 2Zhang J. Sharp conditions of global existence for nonlinear Schrdinger and Klein-Gordon equations[J]. Nonlinear Anal. TMA, 2002, 48:191-207.
  • 3Wang B X. On existence and scattering for critical and subcritical nonlinear Klein-Gordon equations in Hs[J]. Nonlinear Anal. TMA, 1988, 31:573-387.
  • 4Infeld E, Rowlands G. Nonlinear waves, solitons and chaos[M]. Cambridge:Cambridge University Press, 1990.
  • 5Makhankov V G. Soliton phenomenology[M]. Netherlands:Kluwer, Dordrecht, 1990.
  • 6Soffer A, Weinstein M I. Resonance, radiation damping and instability in Hamiltonian nonlinear wave equations[J]. Invent. Math, 1999, 136:9-74.
  • 7Wang X F, Zeng B. On concentration of positive bound states of nonlinear Schrdinger equations with competing potential functions[J]. SIAM J. Math. Anal, 1997, 28(3):633-655.
  • 8Zhang J. Stability of standing waves for nonlinear Schrdinger equations with unbounded potentials[J]. Z. Angew. Math. Phys, 2000, 51:498-503.

同被引文献8

  • 1Pecher H.L^p-Abschtzungen and klassiche Losungen für nichtlineare wellwngeichungen[J].I Math Z,1976,150:159.
  • 2Levine H A.Instability and nonexistence of global solutions of nonlinear wave equations of the form Putt=-Au+F(u)[J].Trans Amer Math Soc,1974,192:1.
  • 3Pagne L E.Sattinger D H.Saddle points and instability of nonlinear hyperbolic equations[J].Isreal Journal of Mathematics,1975,22:273.
  • 4Ball J M.Finite time blow-up in nonlinear problems[C]∥Grandall M G.Nonlinear evolution equations.New York:Academic Press,1978.
  • 5Strass W A.Existence of Solitary waves in higher dimensions[J].Comm Math Phys,1977,55:149.
  • 6Ha J,Nakagiri S.Identification problems for the damped Klein-Gordon equations[J].J Math Anal Appl,2004,289:77.
  • 7Berestycki H,Lion P L.Nonlinear scalar field equations.I.Exitence of ground state[J].Arch Rat Mech Anal,1983,82:313.
  • 8Zhang J.Stability of standing waves for nonlinear Schrodinger equations with unbounded potentials[J].Z Angew Math Phys,2000,51:498.

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四川大学学报（自然科学版）
2005年 第2期

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